Our long-term goal is to quantitatively predict and control circulating leukocyte adhesion to vascular surface, which occurs during both physiological (e.g., leukocyte trafficking and lymphocyte homing) and pathological (e.g., inflammatory responses, atherosclerosis, and tumor metastasis) processes. This adhesion is a complex, multistep cascade that requires interactions with their respective ligands of selectins, which mediate tethering and rolling adhesion, and integrins, which mediate firm adhesion. Extending the parent grant (R01 AI044902, "Kinetic Properties of Selectins", 2000-2005, "Kinetic and Mechanical Properties of al_b2 Integrins", 2005-2010), which focuses on experimental determination of the governing mechanisms and parameters of leukocyte adhesion under flow, here we propose to construct a series of mathematical models of increasing level of sophistication to describe more and more complex cellular functions. These models will integrate these mechanisms and parameters into unifying frameworks to allow us to examine their interplays to extract new information, to relate molecular properties to cellular functions quantitatively, and to predict untested scenarios and suggest new experimental designs. This research will be done primarily at Sun Yat-sen University in Guangzhou, Guangdong, China in collaboration with Professor Jianhua Wu. It has a dual objective: to expand and enhance the parent grant and to increase the research capacity of Dr. Jianhua Wu and his group. The specific aims are (a) to construct models for the analyses of tethering rate and rolling experiments to extract molecular on-rates of selectins and integrins interacting with their respective ligands and (b) to develop models for adhesion patterns on vascular surface, including rolling and firm adhesion as well as transition from the former to the latter, based on the kinetic properties of selectins and integrins. Our approaches include dimensional analysis, mathematical modeling, and numerical simulations. Our strategy is to use simple models at the lower level to construct more complex models at the higher levels. The results of this project promise to improve our understanding of the biophysical bases of the leukocyte adhesion under flow. This improved understanding will provide guidance to the development of strategies for treatment of diseases related to the dysfunction of leukocyte adhesion.